Homotopy theory of stratified spaces
arXiv:1911.04921 · doi:10.2140/agt.2021.21.507
Abstract
In this article, we construct a cofibrantly generated model structure on the category of spaces stratified over a fixed poset, and show that it is Quillen-equivalent to a category of diagrams of simplicial sets. Then, considering all those model structures together, we construct a cofibrantly generated model structure on the category of all stratified spaces. In both model categories, weak-equivalences are characterized by stratified homotopy groups.
26 pages, v2 minor changes and corrections